It says a lot about the duct tube and nothing about the connectors or adapter or whatever.
I’m thinking they are kinda universal. You’ll be ok.
Other than two completely different but both totally common tubing diameters: 3" or 4".
That, you have to get right, at both ends of the duct (dryer and wall).
They’re universal now. How many decades ago was the OP’s residence built and how much shitty temporary work has been put in since? I’ve seen dryer hoses just stuffed into a cutout in the drywall. Yep, the result is blow-in wall “insulation” composed entirely of wildly flammable dryer lint.
OP: the variables are
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Diameter of outlet nozzle on the dryer. The manual will tell you that.
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Whether the dryer has an integral hose or not. The manual will tell you that.
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If not, do you/they already have a dryer hose that fits the dryer outlet nozzle?
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Diameter of vent pipe stub coming out of the wall, if there is one. (if there isn’t one, you’ve got a much larger job that may be beyond Costco’s ability.
If you already have a hose that is built into the dryer, or that fits the dryer, then the only issue is whether the wall pipe stub is the same size. 3" and 4" are the two most common sizes, with 4" being modern. If the same size, they’ll connect with a hose clamp. if not, you’ll need an adapter between the hose size (99% chance it’s 4") and whatever size your wall pipe stub is.
As you can see from the photo link above, there is no stub anymore. I believe that it was like one of bordelond’s first two photos and the installation guy took out the short tube as incompatible with the dryer. Installer provided the hose you see in that picture (I think; I’m fairly sure it’s not from the old dryer, but not sure).
This building is 25 years old.
For the sizes of the adapter, refer to this picture:
The smooth side on the left should be the same size as the dryer tube. The tube will go around that smooth part. The crinkled part on the right will go into the duct in the wall. From your picture of the hole in the wall, the hole in the wall and the tube seem to be about the same size. That adapter you got seems like the crinkled part is smaller than the smooth part. Typically, the dryer tube and the wall duct are both 4", so I would guess that you need an adapter to go 4" to 4". Sometimes the tubes can also be larger. When you go to the hardware store, look at the dryer tubes and see which ones look to be about the same size as yours. That will help you determine what size adapter to get. You may want to get a simple adapter like this:
It’s just a straight tube. The one you got has rotating hinges. That works fine, but it will be bulkier. The straight tube may fit better in the hole in the wall and not protrude out from the wall as far as that twisty one.
The installer said that I needed a “90 degree” one, thus me getting the ones in the photo. The one that’s currently “straight” is the 4” one, which I’m fairly sure the manual says should be the size of the hose.
One question; if the installation was included in the Costco price, was the installer expected to provide any adapters needed or is that on the homeowner?
Depends what “basic installation parts” are to the lawyers. Of course, I wouldn’t have known I’d need one even if it was on me.
Checking the Costco website, it specifies “Basic Installation Parts” as included in the purchase price.
Right, that’s what I was referring to. I couldn’t find on first glance any definition or breakdown.
They ended up leaving that part behind, and I think you’re right. The pictures you posted do look like it.
Welp, round 2 installer came and went, and my dryer still is not hooked up to the wall.
“The last guy should’ve told you that you needed a hose less than five feet. The adapter is just fine. But the hose is too long, so it bends, and pushes the dryer away from the wall so you can’t close the closet door. No, we don’t have any hose besides eight feet. No, we can’t get any.”
Fer cryin’ out loud! Those hoses are the easiest things in the world to cut to length. You’re in some kind of CYA hell. Just find a handyman and send a nasty email to Costco.
I asked about cutting it. They said if they did that, the spring inside would unravel, and so it had to be manufactured to the shorter length.
Edit: So here’s where my inexperience really comes into play: Is it just me? Is all this reasonable, and I’ve just not been responsible enough? I mean, it seems to make sense that Costco can’t possibly have every part to fit every appliance into every space, and it seems kind of silly to send these guys on a shopping excursion.
No. They are, frankly, full of shit. And lazy. You HAVE to cut the wire duck, it comes in long sections, and you cut it to fit. (you want it short as possible, because any bend is another place for lint to build up)
Even in bordelond’s image 3 and 4, with the new fittings (I like those, I wish I had that!), the wire duct is still the same old same old that I have had for 30 years in my house.
This is crap. In the time it took to write this post, if I was your neighbor, I could have had it fixed. And that includes a trip home because I brought the wrong wire cutters. 
Of the broad types of dryer ducts shown below, the aluminum foil flex duct (upper left) and solid metal slim duct (upper right) will cover well over 90% of the installations. The aluminum foil duct tubing absolutely can be cut to size – some brands even advertise the ease of trimming. If the installer really felt the need, they could use … duct tape (!) to seal the cut edge of the foil duct tubing.
All they’d have to have on their service truck is a few 25’ lengths of foil duct tubing, a few slim ducts, maybe one or two semi-rigid ducts (center below) for those use cases, a box of hose connectors/vent rings & screws, and a collection of a half-dozen common adapters (assorted). Stock of these installation items could be kept at Costco, and be replenished in the truck as needed.
Your issues here have nothing to do with materials, but with competence and conscientiousness. Bottom line – Costco should have left your home with your dryer connected and fully usable. You didn’t get what you paid for.
Aside from concurring with all that @bordelond wrote …
This is what we call a “you problem --” with ‘you’ being Costco and their installers.
“The other [Costco-contracted installer] should have told you …”
Gee. Ya’ think?
I’d call Costco at this point, explain the situation, and ask them to make it right.
This ain’t rocket science and you seem to have done nothing wrong.
[TBH, though, because I have it on hand, I’d use foil tape, rather than duct tape, to ‘secure’ the cut end of the wire]
Huh, all the installers seemed to have is a prepackaged eight foot length, presumably directly from the box the dryer came in. That may be why they couldn’t cut it.
A customer service rep called me right after the installers left. The impression that I got was that they considered it my responsibility to have the proper adapter and hose for my particular laundry space, and that they’d happily have the same company come back for a third time to complete the installation once I fulfilled my end of the deal. Which, as I’ve said before, is problematic when I DO NOT KNOW FOR SURE that what I’m buying will work. (See: this morning.)
Cut your losses. Have Costco come out and take the defective machines adn installation back for a 100% refund.
Then go buy machines elsewhere with a real installation service.